Divide the dough into 12 equal-sized pieces. Roll each into a smooth ball. Cover with a cloth towel.
Take one ball of dough and dust it with flour. Roll it into a large round, about 10 inches in diameter.
Using a brush or spoon, scoop out about a teaspoon of the mint stuffing and brush it all over the surface of the rolled out paratha.
Now lift one edge of the paratha and fold it over itself, the way you would if you were making a pleated paper fan. Continue doing this until you've got a long strip. Pinch the edges to seal them.
Beginning at one end, coil the strip into a tight circle. Tuck the other end under the circle and pinch to seal.
Dust the circle of dough with flour and gently roll it into a paratha no more than 5 inches in diameter. The paratha should be fairly thick. If you make it too thin you won't get the flaky layers.
Roast the paratha on a hot cast iron griddle or non-stick griddle until golden-brown spots appear on both sides. Brush with oil or cooking spray.
Stack the cooked parathas as soon as they come off the griddle on a plate, wrapped in a cloth towel or napkin. Keep them wrapped until ready to serve. Before serving, pick each paratha between both hands and lightly push it inward to crush it, separating the layers. Ideally most Indian flatbreads, including pudina paratha, should be eaten right after you make them, but you can store leftovers effectively. See storage instructions below.